After his speech in Jakarta, Obama flew to South Korea and a meeting of the Group of 20 major economic powers in Seoul.

In Indonesia, the world’s most populous Muslim nation, a place where he spent several years as a boy, Obama on Wednesday acknowledged the fraying that remains in U.S.-Islamic relations despite his best efforts at repair. He urged both sides to look beyond “suspicion and mistrust” to forge common ground against terrorism.

Obama praised this nation of islands for progress in rooting out terrorists and combatting violent extremism, and he resurrected a theme he sounded last year during visits to Turkey and Egypt: “I have made it clear that America is not and never will be at war with Islam. … Those who want to build must not cede ground to terrorists who seek to destroy.”

Returning to Indonesia for the first time since 1992, Obama beamed with obvious pride as he delivered what perhaps was the most deeply personal speech of his presidency, including many phrases and words in Indonesian.

“Let me begin with a simple statement: Indonesia is part of me,” he said in the language, cheering the audience of more than 6,000 mostly young people at the University of Indonesia.

At the G-20 summit in Seoul, Obama will find himself on the defensive because of plans by the Federal Reserve to buy $600 billion in long-term government bonds to try to drive down interest rates, spur lending and boost a slow-growing U.S. economy.

Obama has defended the move, which has triggered alarm among leaders from Berlin to Beijing. Critics say the result of the Fed’s action is that American goods will benefit from an unfair competitive edge in world markets.

In his university speech, Obama said he learned to appreciate the “humanity of all” people during the time he spent in Indonesia, with its thousands of islands, hundreds of languages and people from many different regions and ethnic groups.

His brief but nostalgic visit lent an unusually personal touch to the speech, portions of which were devoted to his childhood here. Obama reminisced about living in a small house with a mango tree out front, and learning to love Indonesia while flying kites, running along paddy fields, catching dragonflies and buying food from street vendors.

He also spoke of running in fields with water buffalo and goats, and of the birth of his half-Indonesian sister, Maya.

Obama, a Christian who was born in Hawaii, moved to Indonesia as a 6-year-old and lived with his mother, Stanley Ann Dunham, and Indonesian stepfather, Lolo Soetoro. He attended public and Catholic schools while in Indonesia and returned to Hawaii when he was 10 to live with his grandparents. Obama took care in his remarks to note that he is Christian; back home in the U.S., he continues to fight erroneous perceptions that he is Muslim.

Obama occasionally studied the Quran and visited a local mosque when he lived here. But he spent hardly any time in the speech discussing Islam or his religious background, except to describe Islam as a “great world religion.”

The president’s homecoming had been twice-delayed — first because of the congressional battle over health care and then because of the Gulf of Mexico oil spill. This trip was to be cut short, too, so Air Force One could depart ahead of a big ash cloud from the erupting Indonesian volcano Mount Merapi.

Reaching out to the Islamic world, Obama said efforts to build trust and peace are showing promise but remain incomplete.

He said both sides can choose to either “be defined by our differences and give in to a future of suspicion and mistrust” or “do the hard work of forging common ground and commit ourselves to the steady pursuit of progress.”

On the Middle East, Obama noted the “false starts and setbacks” in getting the peace process between Israel and the Palestinians back on course. But he said the U.S. will “spare no effort in working for the outcome that is just and that is in the interest of all the parties involved: two states, Israel and Palestine, living side by side in peace and security.”

A reminder of that difficult road awaited Obama when he landed in Indonesia on Tuesday. Israel’s decision to build more apartments in east Jerusalem, a disputed territory claimed by Palestinians, had already earned a rebuke from American diplomats before a tired, traveling president weighed in at a news conference with Indonesia’s president.

“This kind of activity is never helpful when it comes to peace negotiations,” Obama said alongside President Susilo Bambang Yudhoyono. “I’m concerned that we’re not seeing each side make the extra effort involved to get a breakthrough. … Each of these incremental steps can end up breaking down trust.”